MULTIGRID MONTE-CARLO .2. 2-DIMENSIONAL XY-MODEL

Abstract

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm applied to the two-dimensional XY model, on lattices up to 128 X 128. In the low-temperature (spin-wave) phase, we find that critical slowing-down is completely eliminated (z = 0). On the high-temperature side of criticality, we find that the dynamic critical exponent is z = 1.4 +/- 0.3, compared to z = 2.1 +/- 0.3 for the heat-bath algorithm. We attribute the remaining critical slowing-down on the high-temperature side of criticality to the limited effectiveness of the MGMC updates in creating and destroying widely separated vortex-antivortex pairs.